%\pgfmathdeclarefunction{cgauss}{2}{%
%  \pgfmathparse{0.5 * (1 - 1/30 * (7*exp(-(x^2)/2) + 16*exp(-x^2 * (2-sqrt(2))) + (7 + 1/4 * pi * x^2)*exp(-x^2) ))}% Bagby (1995)  cdf approximation
%}
\pgfmathdeclarefunction{logisticCDF}{2}{%
  \pgfmathparse{1 / (1 + exp(-(x-#1)/#2))}%
}

\begin{tikzpicture}[scale=1.1]
\begin{axis}[every axis plot post/.append style={%
  domain=-5:5,
  samples=50,
  smooth,
  },
	xmin=-2,
  	xmax=4.5,
  	ymin=0,
  	ymax=1,
	ylabel = {P(\textit{`Signal Present'})},
	xlabel = {Stimulus Strength, $x$},
	ytick={0,.25,.5,.75,1},
	%xtick={-2,0,1,2,4},
	%x tick label style={major tick length=0pt},
	%xticklabels={,0,$\Delta_{lim}$,$\Delta_{lim}$,},
	xtick={-1,0,1,2,3,4},
	xticklabels={-1,0,1,2,3,4},
  % All plots: from -2:2, 50 samples, smooth, no marks
  axis x line*=bottom, 		% no box around the plot, only x and y axis
  axis y line=left,
  enlargelimits=upper,
  legend entries={line 1, line 2, line 3},
  legend pos= south east,
  legend cell align=left,
  legend style={draw=none, font=\scriptsize} % remove border
  ] 		% extend the axes a bit to the right and top

  
  \addplot+[thick,mark=none] {logisticCDF(0,1)};
  \addplot+[thick,mark=none] {logisticCDF(-1,2)};
  \addplot+[thick,mark=none] {logisticCDF(1,1)};

  \draw[dashed, -] ({axis cs:-5,.725}) -- ({axis cs:1.96,.725});
  \draw[dashed, ->] ({axis cs:.96,.725}) -- ({axis cs:.96,0});
  \draw[dashed, ->] ({axis cs:1.96,.725}) -- ({axis cs:1.96,0});
  
  \addplot[only marks, mark=o, color=black] plot coordinates {(-1,0.5)};
  \addplot[only marks, mark=o, color=black] plot coordinates {(0,0.5)};
  \addplot[only marks, mark=o, color=black] plot coordinates {(1,0.5)};
  
\end{axis}
\end{tikzpicture}